> "In group theory, there are discrete and continuous groups. Discrete
> groups are those studied in crystallography and solid-state physics and
> the elements of the group cannot be obtained by means of infinitesimal
> changes. However, the continuous groups are such that finite
> transformation can indeed be made up by infinitesimal transformations.
> Of course, it seems to me that mutations would always involve finite
> changes rather than truly continuous changes."
>
> This is an important point. You have captured exactly the problem that
> many of us have about Darwin's slow series of steps. No one doubts that
> gradual warming causes the river ice to break, or that it can suddenly
> start to crack up on a given day, having been warmed for some time.
> However, some group happenings are, as you say, "discrete."
>

I am trying to understand your arguments and find a relevant analogy - I do
not understand how the behavior of crystals can tell you anyhting about
human gorup behavior, but I can suggest a book, Paul Colinvaux's Fates Of
Nations, A biological theory of history (cambridge u press, 1980). He
provides excellent examples of how advances in technology change the nature
of human competing groups - sudden advances in technology force the response
and refocus of the discipline of a human group as it embraces the new
technology gaining an edge over its competitors. Strict Darwinism only works
at the level of the individual - group behavior is governed by ecology and
niche theory - as individuals specialize in a group they become group
dependent and leaving the group and their niche specialization would cause a
catastrophic drop in their fitness relative to other individuals who are in a
specialized group - its talked about in wilson's book - but colinvaux
provides examples of niche theory at work throughout history
rich